The ability to accurately measure refractive index and dimensions (i.e., thickness) of a sample continues to be in high demand, especially in the areas of precision instrumentation and semiconductor fabrication. Traditionally, for general bulk optics materials, the refractometric-based techniques which measure the minimum diffraction angle of a prism are used; however, such techniques may be limited because they lack the capacity to directly measure a parallel plate sample, which is a common configuration for samples, for example, optical components and semiconductor wafers. Ellipsometers can measure the surface refractive index of a sample. However, the surface refractive index may in fact be quite different from the bulk material. In addition, ellipsometry can be relatively less precise, and ellipsometry signals may be corrupted by reflections beneath the surface.
With regard to thickness measurements, mechanical probes are common industrial tools, but they require physical contact with an object, as compared to non-invasive or non-contact optical techniques. Moreover, mechanical probes typically require access to both sides of a sample, which can be problematic for samples of relatively larger size.
Advances in the fields of optics and semiconductors present significant challenges for currently employed metrology techniques, at least with regard to accuracy and dynamic range requirements. New materials with different and varied geometric structures are emerging at a fast pace, and they often require advanced techniques to accurately determine the refractive index and geometric parameters in a non-invasive manner. Typical interferometer techniques can measure the optical length (i.e., n*d, where “n” represents the refractive index and “d” represents the geometric thickness) of a sample but not the refractive index or geometric thickness separately. As such, multiple techniques may be required in order to accurately extract the refractive index and the geometric thickness from the measured optical length. The increased measurement time as well as the potential for error or inaccuracy introduced by using multiple techniques presents a significant barrier to the use of high resolution interferometer measurements. For example, the National Institutes of Standards and Technology (NIST) conducted an experiment measuring the flatness and geometric thickness variation of silicon wafers. Although the optical thickness had previously been measured to nanometer resolution by a sophisticated interferometer facility, the thickness variation obtained by NIST had a much larger uncertainly of approximately 1 μm, in part because a second interferometer measuring the refractive index variation of the wafers failed to produce results with matching precision.
Shear interferometry can be used to measure thickness and refractive index of a parallel plane plate. The plate may serve as a shear interferometer, which then obtains angle dependant phase shift of a fixed laser beam transmitting through the rotating parallel plane plate. However, such techniques require the sample to be monolayer and to be accessible from both sides thereof. In addition, the measurement accuracy may be limited by the accuracy of the rotation of the sample as well as any interferometer stability issues.
A temporal low-coherence interferometer (T-LCI), or white light interferometer (WLI), is an interferometry technique that may enjoy depth resolving capability, but may lack angle resolving capability. To achieve simultaneous measurements of both refractive index and thickness of a sample, a T-LCI measures the group delay of the sample at a large number of rotation angles. T-LCI techniques thus require the sample or the light source to be rotated through a plurality of angles in order to take a measurement. For certain types of samples and/or processes, such rotation may be inadvisable or unavailable. Less precise thickness measurements can otherwise be obtained by incorporating an apparent thickness measurement taken via microscopic observation. However, such observation invariably requires at least a microscope in addition to the T-LCI system as well as additional time to make such a thickness measurement.